Theorem el021old

Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 13-Jun-2015) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	el021old.1	$$⊢\phi$$
	el021old.2	$$⊢\left(\left(\psi ,\chi \right)\to \theta \right)$$
	el021old.3	$$⊢\left(\phi \wedge \theta \right)\to \tau$$
Assertion	el021old	$$⊢\left(\left(\psi ,\chi \right)\to \tau \right)$$

Proof

Step	Hyp	Ref	Expression
1		el021old.1	$$⊢\phi$$
2		el021old.2	$$⊢\left(\left(\psi ,\chi \right)\to \theta \right)$$
3		el021old.3	$$⊢\left(\phi \wedge \theta \right)\to \tau$$
4	2	dfvd2ani	$$⊢\left(\psi \wedge \chi \right)\to \theta$$
5	1 4 3	sylancr	$$⊢\left(\psi \wedge \chi \right)\to \tau$$
6	5	dfvd2anir	$$⊢\left(\left(\psi ,\chi \right)\to \tau \right)$$